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＜電子ブック＞
Analyzing Markov Chains using Kronecker Products : Theory and Applications / by Tugrul Dayar
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2012.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	2012
大きさ	IX, 86 p. 3 illus : online resource
著者標目	*Dayar, Tugrul author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Numerical analysis LCSH:Computer science—Mathematics LCSH:Mathematical statistics FREE:Probability Theory FREE:Numerical Analysis FREE:Probability and Statistics in Computer Science
一般注記	Introduction -- Background -- Kronecker representation -- Preprocessing -- Block iterative methods for Kronecker products -- Preconditioned projection methods -- Multilevel methods -- Decompositional methods -- Matrix analytic methods Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively HTTP:URL=https://doi.org/10.1007/978-1-4614-4190-8

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